Evaluate cos((17pi)/6)

Problem

cos((17*π)/6)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

(17*π)/6−2*π=(17*π)/6−(12*π)/6

(17*π)/6−(12*π)/6=(5*π)/6

2. Identify the quadrant for the angle (5*π)/6 Since π/2<(5*π)/6<π the angle is in Quadrant II.

3. Determine the reference angle for (5*π)/6 in Quadrant II.

π−(5*π)/6=π/6

4. Apply the cosine sign for Quadrant II. In Quadrant II, the cosine function is negative.

cos((5*π)/6)=−cos(π/6)

5. Evaluate the exact value using the unit circle or special triangles.

cos(π/6)=√(,3)/2

cos((5*π)/6)=−√(,3)/2

Final Answer

cos((17*π)/6)=−√(,3)/2

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